Multivariable function optimization inconsistency

In summary, the conversation discusses a function that is dependent on 4 variables and the process of finding its minima in a specific domain. The conversation also includes a mistake in calculation and how it was solved.
  • #1
RickRazor
17
3
TL;DR Summary
Missing conceptual detail in optimization problems
Mentor note: For LaTeX here at this site, don't use single $ characters -- they don't work at all. See our LaTeX tutorial from the link at the lower left corner of the input text pane.
I have a function dependent on 4 variables . I'm looking to minimize this function in the domain with respect to the variables and .

To find the minima, I first solved and , giving and . Now I have the function of the form

Now I solved for .

So, the final function is of the form which is fine. Now I see later that and .

So, if I directly look for the function and it's minima wrt , it's giving a different result, i.e. I have

even though and . Why is this the case? Are there other simple examples?

The function is
and



,
and .
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Hi,

I have diffculty following the steps; perhaps you can post them ?

And I don't see how can come out: does not exist for ...

 
  • #3
I had made some trivial mistake in calculation. Solved it now. Thanks.
 
  • Like
Likes scottdave
  • #4
RickRazor said:
I had made some trivial mistake in calculation. Solved it now. Thanks.
I'm glad you solved it.

Did it have to do with having r1 in the denominator in one instance then r2 in the denominator in the second instance?
 

FAQ: Multivariable function optimization inconsistency

What is a multivariable function optimization inconsistency?

A multivariable function optimization inconsistency occurs when there is a discrepancy between the expected optimal solution and the actual optimal solution of a function with multiple variables.

How does a multivariable function optimization inconsistency affect the accuracy of results?

A multivariable function optimization inconsistency can significantly impact the accuracy of results, as it indicates that the function may not have a unique optimal solution or that the optimization method used is not effective for the given function.

What are some possible causes of multivariable function optimization inconsistency?

There are several possible causes of multivariable function optimization inconsistency, including incorrect input parameters, inappropriate optimization method, or poorly designed function with multiple local optima.

How can multivariable function optimization inconsistency be addressed?

To address multivariable function optimization inconsistency, it is important to carefully select appropriate input parameters and optimization methods, as well as thoroughly analyze the function to identify any potential issues such as multiple local optima.

What are some techniques that can be used to prevent multivariable function optimization inconsistency?

Some techniques that can help prevent multivariable function optimization inconsistency include sensitivity analysis to determine the impact of input parameters on the optimal solution, using multiple optimization methods to compare results, and carefully designing the function to avoid multiple local optima.

Similar threads

Replies
6
Views
2K
Replies
3
Views
4K
Replies
3
Views
1K
Replies
4
Views
2K
Back
Top